On the Nonlinear Matrix Equation $\boldsymbol{X} + \boldsymbol{A}^∗ f_1(\boldsymbol{X})\boldsymbol{A} + \boldsymbol{B}^∗ f_2(\boldsymbol{X}) \boldsymbol{B} = \boldsymbol{Q}$
Year: 2013
Author: Haifeng Sang, Panpan Liu, Shugong Zhang, Qingchun Li
Communications in Mathematical Research , Vol. 29 (2013), Iss. 3 : pp. 280–288
Abstract
In this paper, nonlinear matrix equations of the form $\boldsymbol{X} + \boldsymbol{A}^∗ f_1(\boldsymbol{X})\boldsymbol{A} + \boldsymbol{B}^∗ f_2(\boldsymbol{X}) \boldsymbol{B} = \boldsymbol{Q}$ are discussed. Some necessary and sufficient conditions for the existence of solutions for this equation are derived. It is shown that under some conditions this equation has a unique solution, and an iterative method is proposed to obtain this unique solution. Finally, a numerical example is given to identify the efficiency of the results obtained.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-CMR-19012
Communications in Mathematical Research , Vol. 29 (2013), Iss. 3 : pp. 280–288
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: nonlinear matrix equation positive definite solution iterative method.